Answers
The upper and lower bounds of each of the numbers are;
1a) Upper bound of 6 = 6.5
Lower bound of 6 = 5.5
b) Upper bound of 83 = 83.5
Lower bound of 83 = 82.5
c) Upper bound of 152 = 152.5
Lower bound of 152 = 151.5
The range as intervals of inequality are;
i) 5.5 ≤ x ≤ 6.5
ii) 82.5 ≤ x ≤ 83.5
iii) 151.5 ≤ x ≤ 152.5
What is the Upper bound and lower bound of the number?The procedure to identify the upper and lower bounds is;
1) Identify the place value of the degree of accuracy stated.
2) Divide this place value by 2.
3) Add this amount to the given value to find the upper bound, subtract this amount from the given value to find the lower bound.
ai) Since it was approximated to the nearest whole number, then we say that the place value of the degree of accuracy is 1.
Divide by 2 to get; 1/2 = 0.5
Upper bound of 6 = 6 + 0.5 = 6.5
Lower bound of 6 = 6 - 0.5 = 5.5
ii) Since it was approximated to the nearest whole number, then we say that the place value of the degree of accuracy is 1.
Divide by 2 to get; 1/2 = 0.5
Upper bound of 83 = 83 + 0.5 = 83.5
Lower bound of 83 = 83 - 0.5 = 82.5
iii) Since it was approximated to the nearest whole number, then we say that the place value of the degree of accuracy is 1.
Divide by 2 to get; 1/2 = 0.5
Upper bound of 152 = 152 + 0.5 = 152.5
Lower bound of 152 = 152 - 0.5 = 151.5
bi) The range as an inequality is;
5.5 ≤ x ≤ 6.5
ii) The range as an inequality is;
82.5 ≤ x ≤ 83.5
iii) The range as an inequality is;
151.5 ≤ x ≤ 152.5
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Related Questions
Decrease £16870 by 3%
Give your answer rounded to 2 DP.
Answers
After decreasing £16870 by 3% we get, £16363.90
Define Percentage.
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
First, find the percentage of £16870 by 3%
%value = 3% * 16870
= (3 / 100) * 16870
= 506.1
Now, just minus with actual value
New value = actual value - %value
We know, actual value = £16870 and %value = 506.1
so, New value = 16870 - 506.1
we get, New value = £16363.90
Therefore, After decreasing £16870 by 3% we get, £16363.90
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what is 2 1/2 - 1 5/6 as an fraction
Answers
The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .
In the question ,
the expression is given as
[tex]2\frac{1}{2} -1\frac{5}{6}[/tex]
To convert a mixed fraction [tex]a\frac{b}{c}[/tex] into a improper fraction , we use the formula
[tex]a\frac{b}{c}[/tex] = (a*c+b)/c
let us first convert the given mixed fraction into improper fraction ,
using the formula of conversion , we get
[tex]2\frac{1}{2}[/tex] = (2*2+1)/2 = 5/2
and
[tex]1\frac{5}{6}[/tex] = (1*6+5)/6 = 11/6
Substituting the values , the expression becomes
= 5/2-11/6
taking the LCM as 6 and solving further , we get
= 15/6 - 11/6
= (15-11)/6
= 4/6
= 2/3
Therefore , The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .
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A car that originally cost $3,668 in 1955 is valued today at $62,125 if in excellent condition, which is 12 times as much as a car in very
nice condition-if you can find an owner willing to part with one for any price.
What would be the value of the car in very nice condition?
Note: Do not round Intermediate calculations.
Value of the car
Answers
The value of the car in very nice condition is $5177.
How to calculate the value?From the information, a car that originally cost $3,668 in 1955 is valued today at $62,125 if in excellent condition, which is 12 times as much as a car in very nice condition.
Let the value of the nice condition car be x
Therefore, the expression will be;
= (12 × x) = 62125
12x = 62125
Divide
x = 62125 / 12
x = 5177
The value is $5177.
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Give me an example of a graph with 4 vertices, with at least one vertex having a degree of 1: ( This is a word problem)
Answers
An example of a graph with 4 vertices, with at least one vertex having a degree of 1 is a square graph.
2K₂= C₄C4 = K2,2There are 11 simple graphs on 4 vertices.
A graph is a set of points, known as vertices, and lines between those points are referred to as edges. there are many exclusive styles of graphs, along with linked and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
This sort of graph with an even wide variety of vertices of diploma 4 has an even length, so our graphs must have 1, three, or 5 vertices of degree four. as much as isomorphism, there is precisely one graph of each type. A related graph G is known as a Hamiltonian graph if there's a cycle that includes each vertex of G and the cycle is referred to as a Hamiltonian cycle. Hamiltonian stroll in graph G is a walk that passes via every vertex precisely as soon as.
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Graph △JKL and its image after a reflection in the line y=−3.
J(3,−5), K(4,−1), L(0,−3)
Answers
The vertices of the image are the points J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3), respectively.
What are the coordinates of the image of a triangle after using a reflection?
Triangles are created by three non-colinear points called vertices and the location of the image of the triangle is found by using a reflection around a line parallel to the x-axis for every point of the figure. This operation is described by the following expression:
P'(x, y) = P(x, y) - 2 · [P(x, y) - (p, k)]
Where:
P(x, y) - Coordinates of the original vertex.p - x-Coordinate of the original vertex.k - y-Coordinate of the equation of the line of reflection.If we know that J(x, y) = (3, - 5), K(x, y) = (4, - 1), L(x, y) = (0, - 3) and k = - 3, then the coordinates of the vertices of the image of the triangle are:
J'(x, y) = (3, - 5) - 2 · [(3, - 5) - (3, - 3)]
J'(x, y) = (3, - 5) - 2 · (0, - 2)
J'(x, y) = (3, - 5) + (0, 4)
J'(x, y) = (3, - 1)
K'(x, y) = (4, - 1) - 2 · [(4, - 1) - (4, - 3)]
K'(x, y) = (4, - 1) - 2 · (0, 2)
K'(x, y) = (4, - 1) + (0, - 4)
K'(x, y) = (4, - 5)
L'(x, y) = (0, - 3) - 2 · [(0, - 3) - (0, - 3)]
L'(x, y) = (0, - 3) - 2 · (0, 0)
L'(x, y) = (0, - 3) + (0, 0)
L'(x, y) = (0, - 3)
The vertices of the image of the triangle are J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3).
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In a sale a TV has been
reduced by 20%. It now costs
£280. How much was it
before the sale?
Answers
Cost of the TV before sale £350
What is a Discount?We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods. Let's examine the connections between these concepts.
Given,
Sale% = 20%
The cost of TV after the sale = £280
Finding the original price:
100% - 20% = 80%
So 80% is the price £280
We have to find the 20% which has been less
Or, £280 = 0.80 x T
Let the original price be T,
280 = 0.80 x T
280/0.80 = T
350 = T
Hence, the original price of the TV was £350.
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Which statement correctly describes the location of the circumcenter of a triangle?
A) The circumcenter is on the inside of an obtuse triangle.
B) The circumcenter is on one of the vertices of an acute triangle.
C) The circumcenter is on the outside of an obtuse triangle.
D) The circumcenter is on one of the sides of an acute triangle.
Answers
Answer:
C) The circumcenter is on the outside of an obtuse triangle.
Step-by-step explanation:
You want to know where the circumcenter is in relation to the sides and vertices of different triangles.
CircumcenterThe circumcenter of a triangle is the center of the circle through its vertices. As such, it will never lie on a vertex of the triangle.
As you can see in the attached figure, the circumcenter of an acute triangle is inside the triangle.
For a right triangle, the circumcenter is the midpoint of the hypotenuse.
The circumcenter of an obtuse triangle is outside the triangle.
__
Additional comment
The circumcenter is located at the point where the perpendicular bisectors of the sides meet.
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Find the y-intercept of the following equation. Simplify your answer.
4x + 5y = 0
Answers
Answer:
y-intercept= (0,0)
Step-by-step explanation:
4x+5y=0
4(0)+5y=0
5y/5=0/5
y=0
4x+5(0)=0
4x/4=0/4
x=0
same for x-intercept (0,0)
compare | 0.525 | and | -0.067 |
Answers
Answer:
|0.525| > |−0.067|
Step-by-step explanation:
Simplifying then comparing both terms |0.525| and |−0.067|, 0.525 is greater than 0.067, which means that the first term is greater than the second term.
The midpoint of CD is M(6, 9). One endpoint is D(2, 10). Find the coordinates of the other
endpoint C.
Answers
endpoint: (14, 28) coordinates of the other endpoint c.
What do the coordinates for midway mean?The x-value at the midpoint lies halfway between the values at the two positions. The y-value midway between the two positions is known as the midpoint.
I start by placing the endpoint coordinate at the top and the halfway coordinate at the bottom.
(2, 10)
(6, 9)
I then calculate the difference between endpoint 1 and the midpoint.
+8 and+19
Applying that to the second coordinate's midpoint
(6 ,9)
8 +19
endpoint: (14, 28)
you can check using the midpoint formula ( x + x / 2, y + y / 2)
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What’s the answer pls
Answers
The opposite of the tangent angle is 10.8cm and the adjacent is p.
Therefore we can input these values into T=O/A…
T=10.8/p
We must also make sure that we enter in our angle, so…
tan(56°)=10.8/p
What is the equation of the line that passes through the point (4,0) and has a slope
of -2
Answers
Answer: y=-2x+8
Step-by-step explanation: Write a table of values where for every x y goes down 2 to find the y intercept (0,8) so it would be 8. The slope is -2 and that is all you need to write the equation.
plus help me I need help with this
Answers
Answer:
a. x=5
b. x=4
Step-by-step explanation:
(3x+4)/2=9.5
3x+4= 19
3x=15
X =5
B)
(7+2x)/3=5
7+2x=15
2x=8
X=4
Which expression is equivalent to 8(x+3)−14(20x−56)
Answers
The equivalent expression of 8(x+3)−14(20x−56) is - 272x + 808.
What are equivalent expression?Two algebraic expressions are equivalent, when the two expressions have the same value when we plug in the same value(s) for the variable(s).
In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.
Therefore, the equivalent expression of 8(x+3)−14(20x−56) can be found as follows;
8(x+3) − 14(20x−56)
open the parenthesis
8x + 24 - 280x + 784
combine the like terms
8x + 24 - 280x + 784
8x - 280x + 24 + 784
Therefore, the equivalent expression is as follows:
- 272x + 808
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Can you help me please it’s. 4 part question but I can only post a picture of one part at a time
Answers
Part a
we have the function
R=-0.1x^3+11x62-100x
using a graphing tool
The answer Part a is 2 turning pointsPart b
we have that
The value of x cannot be a negative number
The value of R can be a negative number
therefore
The answer part b is option Bpart c
the answer part c is the option A and C
Four students were scheduled to give book reports in 1 hour. After tue first report, 2/3 hour remained. The next two reports took 1/6 hour and 1/4 hour. What fraction of the hour remained?
Answers
The fraction of the hour that remained is 1/4 hour.
The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
The students have to submit the book reports in 1 hour.
After the first report, 2/3 hours remained. The next two reports took 1/6 hour and 1/4 hour respectively.
After the first report, 2/3 hours remained.
The next two reports took 1/6 and 1/4 hours.
So, the total time to complete the next two reports is:
= 1/6 + 1/4
= 10/24
= 5/12 hours
Therefore, the fraction of hour remained will be:
= 2/3 - 5/12
= ( 2/3 ) × ( 4/4 ) - 5/12
= 8/12 - 5/12
= 3/12
= 1/4 hour
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what is the significance of finding the n(10) values and absolute ages of the 6 surfaces that the apollo astronauts landed on? select the answer that best addresses the question.
Answers
The surface age. The surface age is the amount of time that has passed between the start of a surface's or interface's creation and the observation or measurement. A continuous probability distribution called a normal distribution has values distributed symmetrically, primarily in an area around the mean.
What exactly does "normal distribution" mean?A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.Because the probability density graph of the normal distribution resembles a bell, it is frequently referred to as the bell curve. In honor of the German mathematician Carl Gauss, who initially characterized it, it is often referred to as the Gaussian distribution.The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.To learn more about Normal distribution refer to:
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calculate the area of parallelogram WXYZ.
Answers
The area of a parallelogram is:
a = bh
The base, b, of the parallelogram is 14.
The issue with this particular figure? We need the perpendicular height. We are given the side width, but that cannot be used in the final equation. So, we employ the Pythagorean Theorem.
We know that in the right triangle, a = 4, and c = 8.
a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
16 - 16 + b^2 = 64 - 16
b^2 = 48
√b^2 = √48
b ≈ 6.93
So, b in this right triangle is equal to h in the parallelogram. So:
a ≈ 14(6.93)
a ≈ 97.02
The iPhone 5s has a base of 58.57 MM and a height of 123.8 3MM find the area of the iPhone 5s round your answer to the nearest hundredths place.help fast plsssss,best answer gets brainiest
Answers
The area of the iPhone 5s in the nearest hundredth is 7252.72 mm².
How to find the area of a rectangle?The iPhone 5s is rectangular in shape and has a base of 58.57 mm and a height of 123.83 mm.
The area of the iPhone 5s can be found as follows:
Therefore,
area of the iPhone 5s = lw
where
l = lengthw = widthTherefore,
l = 58.57 mm
w = 123.83 mm
Hence,
area of the iPhone 5s = 58.57 × 123.83
area of the iPhone 5s = 7252.7231
Therefore,
area of the iPhone 5s = 7252.72 mm²
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Find the value of x
Please show work!!
Answers
Answer:
x = 6
Step-by-step explanation:
8x + 7x = 90
15x = 90
x = 6
The table shows a function. Is the function linear or nonlinear?
Answers
Step-by-step explanation:
a linear function must follow the structure
y = ax + b
we use the given data point numbers for x and y to solve for the 2 variables a and b.
we use 2 data points to get a solution for the 2 variables. if the third data point then fits into the same equation, then all 3 points are on a line, and the function is therefore linear. if not, then not.
-8 2/5 = a×-7 1/2 + b
-6 = a×-1 1/2 + b
let's subtract the second from the first equation to eliminate b and solve for a :
-8 2/5 = a×-7 1/2 + b
- -6 = a×-1 1/2 + b
----------------------------------
-2 2/5 = a×6 0
6a = -2 2/5 = (-2×5 - 2)/5 = -12/5
a = -12/5 / 6 = -2/5
and now we use one of the 2 original equations with the newly found information to solve for b :
e.g.
-6 = -2/5 × -1 1/2 + b = -2/5 × -3/2 + b = 6/10 + b = 3/5 + b
-6 - 3/5 = b
(-6×5 - 3)/5 = b
-33/5 = b
so, our proposed linear function is
y = -2x/5 - 33/5
let's see, if the third point is on the line (then the equality is true for its coordinates) or not :
-2 = -2/5 × 8 1/2 - 33/5 = -2/5 × (8×2 + 1)/2 - 33/5
-2 = -2/5 × 17/2 - 33/5 = -34/10 - 33/5 = -34/10 - 66/10
-2 = -100/10 = -10
that is not true (-2 is not equal to -10), so the third point is not on the line between the first 2 points.
that means the function is nonlinear.
-2x +
= -2x - 6 what is the missing constant?
Answers
Answer:
-6
Step-by-step explanation:
by using -6 any value of x would make the equation true resulting in infinitly many solutions
8.225 - 7.91 please help me
Answers
Answer:
0.315
Step-by-step explanation:
a jar contains 40 marbles and 24 of those marbles are red. If a marble is drawn from the jar at random, what is the probability that the marble picked is red?
Answers
Answer: 60% chance or 3:5
Step-by-step explanation: well, 40/24 is 0.6, which is 60%, or you can see 4 is 10%, and 20 is 50%, and add them together to get 60%. 60% is also 6:10, which can be simplified to 3:5
Annika spends $15.95, Tamara $18.46 and susan $22.80. they are dividing up the expenses equally. how much money should annika give Susan if there equllying the expenses equally
Answers
The amount Annika should give to Susan is $3.12
What is Algebra?
One of the many branches of mathematics is algebra. Algebra is a common thread that runs through nearly all of mathematics. It involves the study of mathematical symbols and the rules for using them in formulas.
Given,
The amount of money Annika spend = $15.95
The amount of money Tamara spend = $18.46
The amount of money Susan spend = $22.80
The total amount of money:
$15.95 + $18.46 + $22.80 = $57.21.
The average money spent :
= $57.21/3
= $19.07 , for each girl.
Thus Annika should give Susan
= $19.07 - $15.95
= $3.12
Hence, Annika should give $3.12 to Susan
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Math pls answer and show work
Answers
Answer:6 trays
Step-by-step explanation:
36 people two cupcakes each means 36x2=72
on tray holds 12 cupcakes 72/12=6 trays
Divide and simplify your answer as much as possible
Answers
[tex]\cfrac{13u^3 y^2 - 32u^2 y}{-4u^3 y^2}\implies \cfrac{13u^3 y^2}{-4u^3 y^2}-\cfrac{32u^2 y}{-4u^3 y^2}\implies -\cfrac{13}{4}+\cfrac{8}{uy}[/tex]
how to solve inequality 3x - y > 2 2x + y > 3
Answers
The graph of an inequality is a region in the Cartesian plane. To know which line is the limit of the graphical region, the inequalities are as if they were equations, that is, graph the following lines:
[tex]\begin{gathered} 3x-y=2\text{ (1)} \\ 2x+y=3\text{ (2)} \end{gathered}[/tex]To do this, first clear y in each of the equations:
First equation
[tex]\begin{gathered} 3x-y=2 \\ \text{ Subtract 3x from both sides of the equation} \\ 3x-y-3x=2-3x \\ -y=2-3x \\ \text{ Multiply by -1 on both sides of the equation} \\ (-y)\cdot-1=(2-3x)\cdot-1 \\ y=-2+3x \end{gathered}[/tex]Second equation
[tex]\begin{gathered} 2x+y=3 \\ \text{ Subtract 2x from both sides of the equation} \\ 2x+y-2x=3-2x \\ y=3-2x \end{gathered}[/tex]Now, give x values that are within the domain of each equation and replace them in each equation to find its corresponding value in y:
First equation
[tex]\begin{gathered} x=-1 \\ y=-2+3x \\ y=-2+3(-1) \\ y=-2-3 \\ y=-5 \\ \text{ Then, you have the ordered pair} \\ (-1,-5) \end{gathered}[/tex][tex]\begin{gathered} x=2 \\ y=-2+3x \\ y=-2+3(2) \\ y=-2+6 \\ y=4 \\ \text{ Then, you have the ordered pair} \\ (2,4) \end{gathered}[/tex]Second equation
[tex]\begin{gathered} x=0 \\ y=3-2x \\ y=3-2(0) \\ y=3 \\ \text{ Then you have the ordered pair} \\ (0,3) \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ y=3-2x \\ y=3-2(3) \\ y=3-6 \\ y=-3 \\ \text{ Then you have the ordered pair} \\ (3,-3) \end{gathered}[/tex]Now, with the points found you can graph the lines that are the limit of the inequalities. So, you have
Finally, it only remains to paint the regions, taking into account the symbols of the inequalities
[tex]\begin{gathered} 3x-y>2 \\ \text{ Subtract 3x from both sides of the equation} \\ 3x-y-3x>2-3x \\ -y>2-3x \\ \text{ Multiply by -1 on both sides of the equation} \\ (-y)\cdot-1>(2-3x)\cdot-1 \\ y<-2+3x \end{gathered}[/tex][tex]\begin{gathered} 2x+y>3 \\ \text{ Subtract 2x from both sides of the equation} \\ 2x+y-2x>3-2x \\ y>3-2x \end{gathered}[/tex]In the case of the first inequality, you can see that y "is less than" the rest of the terms, and in the second inequality, you can see that y "is greater than" the rest of the terms.
Therefore, the graph of the given system of inequalities is
Identify the vertex of each parabola,and then write its corresponding equation.Use the form: y = (x – h) + k
Answers
From the graph we get that:
The vertex of the parabola 1 has coordinates (5,4), and its equation is:
[tex]y=(x-5)^2+4[/tex]
The vertex of parabola 2 has coordinates (-3,-2), and its equation is:
[tex]y=(x-(-3))^2+(-2)=(x+3)^2-2[/tex]Determine the y-intercept of the linear equation 5x + 4y = -40
Answers
5x + 4y = -40
4y = -40 -5x
4y/4 = -40/4 -5x/4
y = -10 -5x/4
hence the y-intercept is -10
Answer:
dog
Step-by-step explanation:
